Fast Kronecker Inference in Gaussian Processes with non-Gaussian Likelihoods

author: Seth Flaxman, Department of Statistics, University of Oxford
published: Sept. 27, 2015,   recorded: July 2015,   views: 32

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Delicious Bibliography


Gaussian processes (GPs) are a flexible class of methods with state of the art performance on spatial statistics applications. However, GPs require O(n3) computations and O(n2) storage, and popular GP kernels are typically limited to smoothing and interpolation. To address these difficulties, Kronecker methods have been used to exploit structure in the GP covariance matrix for scalability, while allowing for expressive kernel learning (Wilson et al., 2014). However, fast Kronecker methods have been confined to Gaussian likelihoods. We propose new scalable Kronecker methods for Gaussian processes with non-Gaussian likelihoods, using a Laplace approximation which involves linear conjugate gradients for inference, and a lower bound on the GP marginal likelihood for kernel learning. Our approach has near linear scaling, requiring O(Dn(D+1)/D) operations and O(Dn2/D) storage, for n training data-points on a dense D > 1 dimensional grid. Moreover, we introduce a log Gaussian Cox process, with highly expressive kernels, for modelling spatiotemporal count processes, and apply it to a point pattern (n = 233,088) of a decade of crime events in Chicago. Using our model, we discover spatially varying multiscale seasonal trends and produce highly accurate long-range local area forecasts.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: